Convergence of Proximal-Gradient Stochastic Variational Inference under Non-Decreasing Step-Size Sequence

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionallyconjugate models. We present a new stochastic method for variational inference which exploits the geometry of the variational-parameter space and also yields simple closed-form updates even for non-conjugate models. We also give a convergence-rate analysis of our method and many other previous methods which exploit the geometry of the space. Our analysis generalizes existing convergence results for stochastic mirror-descent on non-convex objectives by using a more general class of divergence functions. Beyond giving a theoretical justification for a variety of recent methods, our experiments show that new algorithms derived in this framework lead to state of the art results on a variety of problems. Further, due to its generality, we expect that our theoretical analysis could also apply to other applications.